Determination of Wave Function Functionals: The Constrained-Search--Variational Method

In a recent paper [Phys. Rev. Lett. \textbf{93}, 130401 (2004)], we proposed the idea of expanding the space of variations in variational calculations of the energy by considering the approximate wave function $\psi$ to be a functional of functions $\chi: \psi = \psi[\chi]$ rather than a function. The space of variations is expanded because a search over the functions $\chi$ can in principle lead to the true wave function. As the space of such variations is large, we proposed the constrained-search-- variational method whereby a constrained search is first performed over all functions $\chi$ such that the wave function functional $\psi[\chi]$ satisfies a physical constraint such as normalization or the Fermi-Coulomb hole sum rule, or leads to the known value of an observable such as the diamagnetic susceptibility, nuclear magnetic constant or Fermi contact term. A rigorous upper bound to the energy is then obtained by application of the variational principle. A key attribute of the method is that the wave function functional is accurate throughout space, in contrast to the standard variational method for which the wave function is accurate only in those regions of space contributing principally to the energy. In this paper we generalize the equations of the method to the determination of arbitrary Hermitian single-particle operators as applied to two-electron atomic and ionic systems. The description is general and applicable to both ground and excited states. A discussion on excited states in conjunction with the theorem of Theophilou is provided.Comment: 26 pages, 4 figures, 5 table

Equivalent forms of Dirac equations in curved spacetimes and generalized de Broglie relations

One may ask whether the relations between energy and frequency and between momentum and wave vector, introduced for matter waves by de Broglie, are rigorously valid in the presence of gravity. In this paper, we show this to be true for Dirac equations in a background of gravitational and electromagnetic fields. We first transform any Dirac equation into an equivalent canonical form, sometimes used in particular cases to solve Dirac equations in a curved spacetime. This canonical form is needed to apply the Whitham Lagrangian method. The latter method, unlike the WKB method, places no restriction on the magnitude of Planck's constant to obtain wave packets, and furthermore preserves the symmetries of the Dirac Lagrangian. We show using canonical Dirac fields in a curved spacetime, that the probability current has a Gordon decomposition into a convection current and a spin current, and that the spin current vanishes in the Whitham approximation, which explains the negligible effect of spin on wave packet solutions, independent of the size of Planck's constant. We further discuss the classical-quantum correspondence in a curved spacetime based on both Lagrangian and Hamiltonian formulations of the Whitham equations. We show that the generalized de Broglie relations in a curved spacetime are a direct consequence of Whitham's Lagrangian method, and not just a physical hypothesis as introduced by Einstein and de Broglie, and by many quantum mechanics textbooks.Comment: PDF, 32 pages in referee format. Added significant material on canonical forms of Dirac equations. Simplified Theorem 1 for normal Dirac equations. Added section on Gordon decomposition of the probability current. Encapsulated main results in the statement of Theorem

Analyzing 2D gel images using a two-component empirical bayes model

<p>Abstract</p> <p>Background</p> <p>Two-dimensional polyacrylomide gel electrophoresis (2D gel, 2D PAGE, 2-DE) is a powerful tool for analyzing the proteome of a organism. Differential analysis of 2D gel images aims at finding proteins that change under different conditions, which leads to large-scale hypothesis testing as in microarray data analysis. Two-component empirical Bayes (EB) models have been widely discussed for large-scale hypothesis testing and applied in the context of genomic data. They have not been implemented for the differential analysis of 2D gel data. In the literature, the mixture and null densities of the test statistics are estimated separately. The estimation of the mixture density does not take into account assumptions about the null density. Thus, there is no guarantee that the estimated null component will be no greater than the mixture density as it should be.</p> <p>Results</p> <p>We present an implementation of a two-component EB model for the analysis of 2D gel images. In contrast to the published estimation method, we propose to estimate the mixture and null densities simultaneously using a constrained estimation approach, which relies on an iteratively re-weighted least-squares algorithm. The assumption about the null density is naturally taken into account in the estimation of the mixture density. This strategy is illustrated using a set of 2D gel images from a factorial experiment. The proposed approach is validated using a set of simulated gels.</p> <p>Conclusions</p> <p>The two-component EB model is a very useful for large-scale hypothesis testing. In proteomic analysis, the theoretical null density is often not appropriate. We demonstrate how to implement a two-component EB model for analyzing a set of 2D gel images. We show that it is necessary to estimate the mixture density and empirical null component simultaneously. The proposed constrained estimation method always yields valid estimates and more stable results. The proposed estimation approach proposed can be applied to other contexts where large-scale hypothesis testing occurs.</p

Modulation of Serotonin Transporter Function during Fetal Development Causes Dilated Heart Cardiomyopathy and Lifelong Behavioral Abnormalities

BACKGROUND: Women are at great risk for mood and anxiety disorders during their childbearing years and may become pregnant while taking antidepressant drugs. In the treatment of depression and anxiety disorders, selective serotonin reuptake inhibitors (SSRIs) are the most frequently prescribed drugs, while it is largely unknown whether this medication affects the development of the central nervous system of the fetus. The possible effects are the product of placental transfer efficiency, time of administration and dose of the respective SSRI. METHODOLOGY/PRINCIPAL FINDINGS: In order to attain this information we have setup a study in which these parameters were measured and the consequences in terms of physiology and behavior are mapped. The placental transfer of fluoxetine and fluvoxamine, two commonly used SSRIs, was similar between mouse and human, indicating that the fetal exposure of these SSRIs in mice is comparable with the human situation. Fluvoxamine displayed a relatively low placental transfer, while fluoxetine showed a relatively high placental transfer. Using clinical doses of fluoxetine the mortality of the offspring increased dramatically, whereas the mortality was unaffected after fluvoxamine exposure. The majority of the fluoxetine-exposed offspring died postnatally of severe heart failure caused by dilated cardiomyopathy. Molecular analysis of fluoxetine-exposed offspring showed long-term alterations in serotonin transporter levels in the raphe nucleus. Furthermore, prenatal fluoxetine exposure resulted in depressive- and anxiety-related behavior in adult mice. In contrast, fluvoxamine-exposed mice did not show alterations in behavior and serotonin transporter levels. Decreasing the dose of fluoxetine resulted in higher survival rates and less dramatic effects on the long-term behavior in the offspring. CONCLUSIONS: These results indicate that prenatal fluoxetine exposure affects fetal development, resulting in cardiomyopathy and a higher vulnerability to affective disorders in a dose-dependent manner

Atomic processes and application: in honour of David R. Bates' 60th birthday

Atomic Processes and Applications is a collection of review articles that discusses major atomic and molecular processes and their applications to upper atmospheric physics and to astrophysics. The book also serves as a 60th birthday tribute to Dr. David R. Bates. The coverage of the text includes the overview of stratospheric aeronomy; upper atmosphere of the earth; and problems in atmospheric pollution. The book also deals with technical and highly specialized issues including photoionization of atomic systems; atomic structure and oscillator strengths; and atomic scattering computations. T